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MOTION OF ;A PARTICLE                       121
Therefore the component of jthe velocity along the ;r-axis remains constant, while the ' component along the y-axis changes uniformly. Let VQ be the velocity of projection, then when t = 0, x = VQ cos a and y = VQ sin a. Making these substitutions in the last two equations we obtain
and
Therefore
and
Ci = VQ COS a,
c2 = VQ sin a.
X= VQ COS Ctj
y = VQ sin a -
FIG. 66. Therefore the total velocity at any instant is
2~-2v0gsma-t+gH*\ and makes an angle 0 with the horizon defined by
V        '
,
rc     t;0sina ^t
Integrating equations (3) and (4) we obtain
X = #o COS a   + Cs,
and                       y = z;0 sin a  35- f ffi2+ c4.
But when * = 0, a; = y = 0, therefore c3 = c4 == 0, and consequently
x = VQ cos a  t,                                          (7)
y = z;0 sin a  t - | gtf2.                              (8)-